# Properties

 Label 69696.cd Number of curves 4 Conductor 69696 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("69696.cd1")

sage: E.isogeny_class()

## Elliptic curves in class 69696.cd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
69696.cd1 69696gq4 [0, 0, 0, -3068076, -2068459184]  1474560
69696.cd2 69696gq3 [0, 0, 0, -454476, 72811024]  1474560
69696.cd3 69696gq2 [0, 0, 0, -193116, -31837520] [2, 2] 737280
69696.cd4 69696gq1 [0, 0, 0, 2904, -1650440]  368640 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 69696.cd have rank $$0$$.

## Modular form 69696.2.a.cd

sage: E.q_eigenform(10)

$$q - 2q^{5} + 4q^{7} + 6q^{13} + 6q^{17} + 8q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 